So I fixed up my math to reflect the probabilities of the original result being higher/lower, and it's actually slightly higher than 70%.

The optimal strategy changes as you gain information, which isn't account for when you go through your case. When you say 5, the higher/lower isn't 50% like you said. This means that the probability of you picking 3 or 8 isn't split 50%. 44.44% of the time you will pick 3, and 55.66% of the time you will pick 8. If you pick 8, then you will guess between 6/7 or 9/10. That's 50/50. But the 44.44% of the time you pick 3, 33.3% of the time you win immediately (you're told it's higher, aka 4) and 66.7% of the time you would have to make your guess between 1 or 2.